In this work, a geometrical representation of equilibrium and near equilibrium classical statistical mechanics is proposed. Within this formalism the equilibrium thermodynamic states are mapped on Euclidian vectors on a manifold of spherical symmetry. This manifold of equilibrium states can be considered as a Gauss map of the parametric representation of Gibbs classical statistical mechanics at equilibrium. Most importantly, within the proposed representation, out of equilibrium thermodynamic states, can be described by a triplet consisting of an ‘infinitesimal volume’ of the points on our manifold, a Euclidian vector that points on the equilibrium manifold and a Euclidian vector on the tangent space of the equilibrium manifold. Finally in this work we discuss the relation of the proposed representation to the pioneer work of Ruppeiner and Weinhold at the limit of equilibrium, along with the notion of K–L divergence and its relation to the second law of thermodynamics.

在这项工作中，提出了平衡和接近平衡的经典统计力学的几何表示。在这种形式主义中，平衡热力学状态映射​​在球对称的流形上的欧几里得向量上。这种平衡状态的流形可以看作是吉布斯古典统计力学在平衡状态下的参数表示形式的高斯图。最重要的是，在提出的表示中，不平衡热力学状态可用三元组描述，该三元组由流形上点的“无穷大”，平衡流形上的欧几里得矢量和切线上的欧几里得矢量组成平衡流形的空间。